Other mistake: Two Borg are discovered North of the Arctic Circle. One is covered in ice, the other encased in ice. Carbon dating shows the wreckage to be over 100 years old (to tie it in with Star Trek:First Contact). The Borg are inactive and unable to repair themselves until they are "defrosted". The temperature above the Arctic Circle doesn't usually drop below -100°F. The Borg have been shown to work very well in the vacuum of space which is 3-4K (roughly -454°F). If they can survive that, even being frozen in a solid block of ice would not slow them down. The nanites have to be in their "blood" and operate at the cellular level. That cannot be damaged by re-entry and the crash. [This is one of those entries that keeps being corrected and recorrected - I'll leave it up to people to make up their own minds.]
Other mistake: As Archer, T'Pol and the ambassador are having dinner, the Ambassador inquires about who previously occupied the cabin (that she was to be staying in). T'Pol assumes this is regarding concerns about human "odor", but the ambassador says, "Actually I was hoping to meet the crew member in order to thank her for allowing me to disrupt her routine." However, the ambassador has no way of knowing what gender the crew member is, as no mention of this person has been made. Although the crew member was, in fact, Hoshi (who is female), the ambassador would not have known this, and had no reason to refer to the crew member as "her". (00:08:34)
Other mistake: They show the tether and tether anchor fall out of the ship and fall behind, much in the same way as throwing something out of a car. However, it was still in the warp bubble and should have continued to be moving at warp 5 with the ships. We see later Columbia extend its warp bubble around Enterprise and Enterprise remains at warp 5 after cutting their engines. But, if the tether is no longer affected by the warp bubble, it should have been instantaneously out of view.
Other mistake: Just as Malcolm finishes opening the hatch on the alien pod, a graphical mistake appears towards the left side of T'pol's arm. It appears as if a section of the craft had been added with an overlay, which abruptly disappears as the cutting tool stops firing. (00:01:30)